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lfunc_lfunctions • Show schema
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{'Lhash': '1710893447900688158001232932877', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.4142135623730951, -1.0], 'a4': [0.0, 0.0], 'a5': [1.7320508075688772, 1.4142135623730951], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, -2.8284271247461903], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.665638594042921, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.4142135623730951, 1.0]]], [5, [[1.0, 0], [-1.7320508075688772, -1.4142135623730951]]]], 'bad_primes': [2, 3, 5], 'central_character': '960.959', 'coefficient_field': 'CDF', 'conductor': 960, 'conductor_radical': 30, 'conjugate': '1959744960807694135703102626173', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.4142135623730951, 1.0]], [[1.0, 0], [-1.7320508075688772, -1.4142135623730951]], [[1.0, 0], [0, 0], [7.0, 0]], [[1.0, 0], [-4.898979485566356, 0], [11.0, 0]], [[1.0, 0], [0, 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[[1.0, 0], [-2.0, 0], [109.0, 0]], [[1.0, 0], [3.4641016151377544, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 26, 'label': '2-960-60.59-c1-0-26', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/960/2/o/d/959/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.5466675750574326, 2.526486791235586, 2.485966422687909, 2.416621112427816, 2.3069458557870393, 2.1448748934817834, 1.9203605953713445, 1.6277095136315427, 1.2674643302654294, 0.8476919770903873, 0.38454875941382066, -0.09800703129313817, -0.5694583636358297, -0.994963858673234, -1.3385102490430234, -1.5667737430466158, -1.65333714175383, -1.582782055642407, -1.3540907471329293, -0.9827744229922495, -0.501212661060102, 0.04314984370229286, 0.591853886650263, 1.0815138085760414, 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'7.71377984332650204444860598032310', '8.610561109615001691559391804060768', '9.287459736505532438049453850675466', '9.709265356310864495015056189015166'], 'prelabel': '2-960-60.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.768688966648822, 'root_angle': 0.0220396155602089, 'root_number': '0.9976039037037866 + 0.06918418399436431*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0110198077801', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.34965695404763486023126385774', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.61531076316282649256860049527', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73119983478107147034021217367', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.665638594042921, 'bad_primes': [2, 3, 5], 'central_character': '60.59', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/960/2/o/d/959/6'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-960-60.59-c1-0-26', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-960-60.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.768688966648822, 'root_angle': 0.01101980778010445, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34965695404763486023126385774', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1710893447900688158001232932877', 'Lhash_array': ['1710893447900688158001232932877'], 'label': '2-960-60.59-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/2/o/d/959/6'}